Question

An automobile assembly line operation has a scheduled mean completion time, H, of 12 minutes. The standard deviation of completion times is 1.2 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 41 completion times under new management was taken. The sample had a mean of 11.9 minutes. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: 31 р x s The alternative hypothesis: 5 De 8 Da The type of test statistici OSO 020 (Choose one) Ova D D d> The value of the test statistic (Round to at least three decimal places) 0 X ? The critical value at the 0.01 level of significance (Round to at least three decimal places) D Can we support the claim that the mean completion time has decreased under new management? Yes No

Answer 1

Solution Given data X=11.9 n=41 L=0.01 This is one-tailed test Now to state the mult and altermative hypothesis Null hypothesis Ho: M =12 Altermative hypothesis H: <12 It is left-tailed" test test Statistic is "?" * Now to find the value of the zis given by The formula of test statistic * The type of test statistic We know that 11.9 - 12 Z= 1.21 VF - 0.1 0.1874 Z = -0.534 Therefore the value of the test statistic is (-0.534

Now critical Value Decision to find the Z critical value: Z =- 2.326 The critical value at the door level of significance is (-2.326| Z critical < Test statistic - 2.326 < -0.534 Since z koritical value is less than the Test statistic (Z). Therefore reject the null hypothesis Ho. conclusion : Yes we support the claim that the mean completion time has decreased under new management. we